episciences.org_650_1635092793
1635092793
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
03
15
2016
Vol. 18 no. 3
Automata, Logic and Semantics
Factoriality and the Pin-Reutenauer procedure
J.
Almeida
J. C.
Costa
M.
Zeitoun
We consider implicit signatures over finite semigroups determined by sets of
pseudonatural numbers. We prove that, under relatively simple hypotheses on a
pseudovariety V of semigroups, the finitely generated free algebra for the
largest such signature is closed under taking factors within the free pro-V
semigroup on the same set of generators. Furthermore, we show that the natural
analogue of the Pin-Reutenauer descriptive procedure for the closure of a
rational language in the free group with respect to the profinite topology
holds for the pseudovariety of all finite semigroups. As an application, we
establish that a pseudovariety enjoys this property if and only if it is full.
03
15
2016
650
arXiv:1506.01074
10.46298/dmtcs.650
https://dmtcs.episciences.org/650